Chi Square Test

The chi-square test of independence compares observed and expected frequencies in a contingency table to test whether two categorical variables are associated.

카이제곱 독립성 검정은 분할표의 관측빈도와 기대빈도를 비교하여 두 범주형 변수가 서로 연관되어 있는지를 검정하는 방법이다.

How do I test whether two categorical variables are related?

두 범주형 변수 사이에 관련이 있는지 어떻게 검정하나요?

The chi-square test of independence tests whether two categorical variables are associated by comparing observed cell counts with the counts expected if they were independent. It fits when each observation falls into exactly one cell of a cross-tabulation and expected counts are large enough.

When to use Chi Square Test

• Cross-tabulating two categorical variables such as group and response category
• Comparing proportions of an outcome across two or more independent groups
• Survey items with nominal answer options classified by respondent group

When to use something else

• Expected cell counts are small (for example in a 2x2 table): use Fisher's exact test
• The same subjects are measured twice on a binary variable: use McNemar's test

Assumptions and requirements

• Observations are independent and each falls into one cell only
• Expected count is at least 5 in most cells (conventionally at least 80% of cells and none below 1)
• Data are frequencies, not percentages or means

What the analysis reports

• Chi-square statistic with degrees of freedom and p-value
• Observed and expected counts per cell
• Standardized or adjusted residuals by cell
• Effect size such as Cramer's V or phi

How to report it

A chi-square test of independence showed a significant association between [variable 1] and [variable 2], χ²([df], N = [n]) = [value], p = [value], Cramér's V = [value].

Related methods

• Fisher's Exact Test
• McNemar's Test
• Cramér's V

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